Problem: Luis is 3 times as old as William. Twenty years ago, Luis was 7 times as old as William. How old is William now?
Answer: We can use the given information to write down two equations that describe the ages of Luis and William. Let Luis's current age be $l$ and William's current age be $w$ The information in the first sentence can be expressed in the following equation: $l = 3w$ Twenty years ago, Luis was $l - 20$ years old, and William was $w - 20$ years old. The information in the second sentence can be expressed in the following equation: $l - 20 = 7(w - 20)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $w$ , it might be easiest to use our first equation for $l$ and substitute it into our second equation. Our first equation is: $l = 3w$ . Substituting this into our second equation, we get: $3w$ $-$ $20 = 7(w - 20)$ which combines the information about $w$ from both of our original equations. Simplifying the right side of this equation, we get: $3 w - 20 = 7 w - 140$ Solving for $w$ , we get: $4 w = 120.$ $w = 30$.